"In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities."
The study of the behavior of large numbers of particles, based on the laws of classical physics.
Introduction to statistical mechanics: Statistical mechanics is a fundamental framework for understanding the behavior of systems consisting of a large number of particles. This topic provides an overview of the principles, concepts, and methods of statistical mechanics.
Probability theory: Probability theory is a branch of mathematics that deals with the study of random events. This topic covers the basic probability concepts and distributions necessary for statistical mechanics.
Thermodynamics: Thermodynamics is the science of energy transfer and transformation. This topic covers the fundamental laws of thermodynamics and their application to statistical mechanics.
Kinetic theory: Kinetic theory is a branch of statistical mechanics that describes the behavior of a large number of particles in terms of the motion of individual particles. This topic covers the derivation of the kinetic theory equation and its applications.
Ensemble theory: Ensemble theory is the study of the behavior of ensembles of particles rather than individual particles. This topic covers the different ensembles used in statistical mechanics and their properties.
Partition functions: Partition functions are mathematical functions that describe the statistical properties of a system. This topic covers the derivation and use of partition functions in statistical mechanics.
Statistical mechanics of gases: The statistical mechanics of gases is the study of the thermodynamic behavior of gases at the molecular level. This topic covers the ideal gas law, the Maxwell-Boltzmann distribution, and the statistical mechanics of real gases.
Classical ideal gas: The classical ideal gas is a simplified model for the behavior of a gas that consists of a large number of non-interacting particles. This topic covers the thermodynamic properties of the classical ideal gas and its application to real gases.
Quantum ideal gas: The quantum ideal gas is a model for the behavior of a gas that consists of a large number of non-interacting particles obeying quantum mechanics. This topic covers the thermodynamic properties of the quantum ideal gas and its application to real gases.
Probability distribution functions: Probability distribution functions are mathematical functions that describe the probability of particles occupying different energy levels. This topic covers the derivation and use of probability distribution functions in statistical mechanics.
Canonical ensemble: The canonical ensemble is a statistical ensemble in which the number of particles and the temperature are fixed. This topic covers the derivation of the canonical partition function and its applications.
Grand canonical ensemble: The grand canonical ensemble is a statistical ensemble in which the number of particles, the volume, and the chemical potential are fixed. This topic covers the derivation of the grand canonical partition function and its applications.
Quantum statistics: Quantum statistics is the study of the statistical behavior of particles that obey quantum mechanics. This topic covers the Fermi-Dirac and Bose-Einstein statistics and their applications.
Phase transitions: Phase transitions are changes in the physical properties of a system that occur when a parameter, such as temperature or pressure, is varied. This topic covers the different types of phase transitions and their description using statistical mechanics.
Fluctuations: Fluctuations are the random deviations of a system's properties from their average values. This topic covers the derivation and applications of the fluctuation relations in statistical mechanics.
Nonequilibrium statistical mechanics: Nonequilibrium statistical mechanics is the study of the behavior of systems that are not in thermal equilibrium. This topic covers the different approaches to nonequilibrium statistical mechanics, such as the Green-Kubo formula and the linear response theory.
Canonical ensemble: This statistical mechanics approach describes a closed thermodynamic system in which the temperature, volume and number of particles are held constant, but the internal energy may fluctuate. This approach is particularly useful in describing systems consisting of a large number of identical particles in equilibrium with a heat reservoir.
Grand Canonical ensemble: This statistical mechanics approach describes a system with a fixed volume and temperature, but which has an open particle number. This approach is particularly useful in describing systems that can exchange particles with their surroundings, such as a gas at a fixed temperature and pressure in contact with a reservoir of particles.
Microcanonical ensemble: This statistical mechanics approach describes a system consisting of a fixed number of particles, with no exchange of particles or heat with its surroundings, and with a fixed total energy. This approach is useful for describing systems where the energy is well defined, such as an isolated system or an ideal gas in a container with no exchange of heat or particles.
Ising model: This statistical mechanics approach describes a system consisting of spins in a lattice, where each spin can have two possible states (up or down). The Ising model is commonly used to describe the magnetization behavior of ferromagnetic materials.
Monte Carlo simulations: This is a computational technique used to simulate the behavior of systems at a microscopic level, typically using a large number of random samples or "events". Monte Carlo simulations are commonly used in statistical mechanics to describe the behavior of complex systems such as fluids, materials or biological systems.
Molecular Dynamics simulations: This is a computational technique used to simulate the motion of molecules in a system. Molecular Dynamics simulations are commonly used in statistical mechanics to describe the dynamics of large biological molecules, fluids or materials.
Density Functional Theory: This is a computational approach used to determine the electronic structure and energy of a system based on its density. Density Functional Theory is commonly used in statistical mechanics to describe the behavior of electrons in materials or molecules.
Quantum Monte Carlo: This is a computational technique used to simulate the behavior of quantum mechanical systems at a microscopic level, typically using a large number of random samples or "events". Quantum Monte Carlo simulations are commonly used in statistical mechanics to describe the behavior of complex quantum systems such as solids, molecules or superconductors.
Path Integral Monte Carlo: This is a computational technique used to simulate the behavior of quantum mechanical systems at a microscopic level, by expressing the quantum mechanical behavior of particles in terms of a path integral. Path Integral Monte Carlo simulations are commonly used in statistical mechanics to describe the behavior of Bose-Einstein condensates, superfluids or other quantum systems.
"It explains the macroscopic behavior of nature from the behavior of such ensembles."
"Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience."
"Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion."
"Statistical mechanics arose out of the development of classical thermodynamics."
"Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates."
"James Clerk Maxwell, who developed models of probability distribution of such states."
"Josiah Willard Gibbs, who coined the name of the field in 1884."
"Non-equilibrium statistical mechanics focuses on the issues of microscopically modeling the speed of irreversible processes that are driven by imbalances."
"Examples of such processes include chemical reactions and flows of particles and heat."
"The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles."
"It applies statistical methods and probability theory."
"It does not assume or postulate any natural laws."
"It explains the macroscopic behavior of nature from the behavior of such ensembles."
"Classical thermodynamics is primarily concerned with thermodynamic equilibrium."
"Microscopic parameters fluctuate about average values and are characterized by probability distributions."
"It clarifies the properties of matter in aggregate, in terms of physical laws governing atomic motion."
"Physics, biology, chemistry, and neuroscience."
"Microscopically modeling the speed of irreversible processes that are driven by imbalances."
"Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs."